When you move the root from node to its child :
Nodes in 's subtree get closer (they're now below the root instead of edges away).
All other nodes get farther (they have to go through now). If 's subtree has nodes, then nodes get farther. So: .
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$ curl repovive.com/roadmaps/dynamic-programming/dp-on-trees/sum-of-distances-key-observation
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